Overview of None Trend

Lets just review the overall trend of more people claiming no religious affiliation in the GSS.

Percentage of respondents in the GSS with no religious affiliation. Smoothed (LOWESS) trend shown in grey. All percentages are sample weighted.

Percentage of respondents in the GSS with no religious affiliation. Smoothed (LOWESS) trend shown in grey. All percentages are sample weighted.

Belief in God

To begin, lets look at the trend across all six categories for the religiously affiliated and the nones. Because this will get very noisy with lots of points, I will just show LOWESS-smoothed lines for all trends.

The results for the affiliated are pretty clear - there is not much change over time. The only notable change is prehaps a slight decline in more recent years and an uptick in people who believe in a “higher power.”

The results get a bit noisy for the nones, as one would expect given the smaller sample sizes. Still I note a couple of interesting things. First, the agnostic and aethist smoothed lines are almost mirror images of one another - when one is increasing the other is decreasing. As a result when you add them up there isn’t much change over time, but this might be deceiving. Overall, before 2000, the agnostic response was on the decline and the aethist on the rise. This switched after 2000, but now may be turning around again with a noticeable uptick in the aethist category since 2010 and a leveling off of the agnostic response. Second, before 2000, the most confident category of belief in god actually increase the most while the other two categories declined (believe sometimes) or were stationary. In combination with the pattern for aethist responses, this suggests greater polarization before 2000. Since 2000, all of the believer categories have been on the decline, while higher power has increased substantially. Overall, “spiritual but not religious” (higher power) and agnostic responses are the two most common responses throughout most of the time period, except for the period in which those who “know god exists” rose.

It will be very difficult to fit a model to all six categories and get anything meaningful, but lets go ahead and try a cumulative logit model with the assumption of parallel effects to see how well it does.

Cumulative logit models with parallel effects predicting belief in god using all six categories
(1) (2)
nonesNone -2.382*** -2.340***
(0.048) (0.088)
year.centered -0.002 0.014**
(0.002) (0.005)
year.spline -0.025**
(0.008)
nonesNone_year.centered -0.006 0.006
(0.004) (0.014)
nonesNone_year.spline -0.015
(0.020)
Observations 22275 22275
BIC 49919.9 49925.6
Note: p<0.05; p<0.01; p<0.001

How well does it fit the trends for the nones?

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded
## `geom_smooth()` using method = 'loess'

Yes, both fits are pretty shit. So that means I need to either estimate non-parallel effects in the cumulative logit models or I could switch to a multinomial model, which also allows for non-parallel effects by default. However, in both cases the number of categories is going to make it difficult because of statistical noise for then nones, so I will collapse the six-category question on belief in god into three ordinal categories:

  1. Non-belief: “Don’t believe” or “No way to Find out”
  2. Higher Power: “Some higher power”
  3. Belief: “Believe sometimes”, “Believe but doubts”, or “Know god exists”

I first try out some cumulative logit models. I fit a linear trend model and a spline model and for each o these cases I also fit a version that forces parallel effects and one that allows effects to vary across cutpoints.

Cumulative logit models predicting belief in god
(1) (2) (3) (4)
nonesNone -2.548*** -2.491***
(0.052) (0.101)
year.centered -0.003 0.007
(0.003) (0.008)
year.spline -0.016
(0.013)
nonesNone_year.centered -0.006 0.007
(0.005) (0.016)
nonesNone_year.spline -0.018
(0.023)
nonesNone_1 -2.609*** -2.559***
(0.067) (0.137)
nonesNone_2 -2.500*** -2.431***
(0.055) (0.107)
year.centered_1 0.006 0.015
(0.004) (0.014)
year.centered_2 -0.004 0.006
(0.003) (0.008)
year.spline_1 -0.014
(0.021)
year.spline_2 -0.016
(0.013)
nonesNone_year.centered_1 -0.010 0.002
(0.006) (0.021)
nonesNone_year.centered_2 -0.010* 0.005
(0.005) (0.017)
nonesNone_year.spline_1 -0.016
(0.031)
nonesNone_year.spline_2 -0.021
(0.025)
Observations 22275 22275 22275 22275
BIC 22538.7 22554.1 22553.3 22588.5
Note: p<0.05; p<0.01; p<0.001

I am finding these cumulative logit models a little difficult to interpret, particularly around the higher power issue. Lets just try multinomial logit models with non-believers set as the reference category. This will give me a better sense of whats happening with the non-believer vs. higher power bit.

Multinomial logit models with non-believer as the reference category
higher power believer higher power believer
(1) (1) (2) (2)
year.centered 0.014** 0.005 0.011 0.014
(0.005) (0.004) (0.017) (0.014)
nonesNone -0.925*** -3.013*** -0.868*** -2.915***
(0.083) (0.071) (0.167) (0.144)
year.spline 0.003 -0.013
(0.026) (0.021)
year.centered:nonesNone -0.007 -0.016* 0.003 0.004
(0.008) (0.007) (0.026) (0.022)
nonesNone:year.spline -0.015 -0.029
(0.038) (0.032)
Constant 0.678*** 3.263*** 0.665*** 3.317***
(0.053) (0.044) (0.119) (0.099)
Note: p<0.05; p<0.01; p<0.001

The results here suggest, like the cumulative logit models, that the spline model isn’t doing much here. A linear trend model fits better. That linear trend model shows that the nones are increasingly less likely to believe in god, but there is little evidence that they are less likely to believe in a non-personal higher power. So, how you think about this one depends largely on how you view that higher power question.

Now, I will plot a figure that sees how well the linear and spline model fit the data over time for each group. I am going to show the fit of both the multinomial logit model and the cumulative logit models that assumed parallel effects across cutpoints. I leave out the cumulative logit models that allowed effects to vary because these are virtually the same as the multinomial logit results.

Percent of respondents who held given beliefs about god, separated by those with a religious affilation and those without. Fit of multinomial logit models with a linear trend (light grey) and a spline with a hinge at 2000 (dark grey) are also shown. Fit of cumulative logit models with parallel effects with a linear trend (light red) and a spline (dark red) are also shown.

Percent of respondents who held given beliefs about god, separated by those with a religious affilation and those without. Fit of multinomial logit models with a linear trend (light grey) and a spline with a hinge at 2000 (dark grey) are also shown. Fit of cumulative logit models with parallel effects with a linear trend (light red) and a spline (dark red) are also shown.

Its easy to see that the cumulative logit models with parallel effects fit the trend of higher power among the nones very poorly and ends up going in the wrong direction. the linear multinomial logit models seem to fit well. There is more evidence of a broken arrow between the non-belief and belief category than the higher power but linear trends also fit this well.

I think the stronger broken arrow in the figure with the scoring method is because of some shifts within the big categories of non-believers and believers. In particular, among the non-affiliated believers tended to shift toward believing in god without doubt and away from the more ambivalent categories of belief.

Belief in Afterlife

Lets plot up the percentages by all three categories to see what is going on.

Most of the action seems to be captured by the yes/no difference. There may be some slight rise in don’t know before 2000 which then levels off after 2000. Lets try fitting three separate cumulative logit models. - parallel effects and a linear trend - parallel effects and a spline term - non-parallel effects and a spline term

Cumulative logit models predicting belief in afterlife using all three categories
(1) (2) (3)
nonesNone -1.292*** -1.138***
(0.029) (0.056)
year.centered 0.010*** 0.011***
(0.001) (0.002)
year.spline -0.003
(0.004)
nonesNone_year.centered -0.004 0.008
(0.002) (0.004)
nonesNone_year.spline -0.029**
(0.009)
nonesNone_1 -1.004***
(0.063)
nonesNone_2 -1.238***
(0.058)
year.centered_1 0.017***
(0.002)
year.centered_2 0.010***
(0.002)
year.spline_1 -0.009
(0.005)
year.spline_2 -0.002
(0.004)
nonesNone_year.centered_1 0.010*
(0.005)
nonesNone_year.centered_2 0.005
(0.005)
nonesNone_year.spline_1 -0.035***
(0.010)
nonesNone_year.spline_2 -0.023*
(0.009)
Observations 44460 44460 44460
BIC 66509.1 66513.8 66412.8
Note: p<0.05; p<0.01; p<0.001

The spline models both fit well regardless of whether we use parallel or non-parallel effects. In the non-parallel case the effects all seem stronger (except for the none dummy) for the first cutpoint between no and don’t know, but I still get the same basic result if I cut at don’t know and yes.

Lets look at how well the models fit. The light grey shows the fit of the parallel spline model and the dark grey shows the fit of the non-parallel spline model.

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded
## `geom_smooth()` using method = 'loess'

The parallel model has some fit problems for the DK category for nones. Nonetheless, I don’t think it is necessary to move to a different model here as the results are pretty consistent across at each cutpoint. Both the don’t know and yes categories rose relative to no before 2000 and both fell relative to the no category after 2000.

Frequency of Prayer

According to the GSS explorer, before 2004, “Never” was not offered as a pre-coded response, but only recorded if volunteered by the respondent. For this reason, I have followed the GSS recommendation of collapsing “Never” and “Less than once a week” for analysis across the entire time period to produce more consistent results.

First, I look at the smoothed trend lines across all five categories for both groups.

## `geom_smooth()` using method = 'loess'

Most of the action seems to be happening in the at least once a day and less than once a week categories. There is some decline in the weekly categories for both groups but no indication of non-linearity. So evidence of polarization for both groups in terms of prayer: you either pray once a day or you just don’t really bother - nothing god hates like wishy-washy praying.

As for the belief in god section, I will first try to fit a cumulative logit model with parallel effects to all of the categories.

Cumulative logit models with parallel effects predicting frequency of prayer using all five categories
(1) (2)
nonesNone -2.160*** -1.997***
(0.036) (0.070)
year.centered 0.014*** 0.010***
(0.001) (0.002)
year.spline 0.009*
(0.004)
nonesNone_year.centered -0.0002 0.019*
(0.003) (0.008)
nonesNone_year.spline -0.035**
(0.013)
Observations 33056 33056
BIC 95161.3 95173.2
Note: p<0.05; p<0.01; p<0.001

How well does it fit the data?

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded
## Warning: Ignoring unknown parameters: spane
## `geom_smooth()` using method = 'loess'

The fit is not horrible here but it does seem to be missing the trend and the level for the weekly values for the none and also mising the trend a bit for several times a day for the nones. So, I follow the same procedure as for belief in god in collapsing the number of categories and testing models with less constraints.

I collapsed the five-category prayer variable into a three category variable of:

  1. less than once a week: those who said “never” or “less that once a week”. There was almost no-one in the “never” category until 2004 so I suspect something in the question wording shifted here. I need to check this.
  2. weekly: those who said “once a week” or “several times a week”.
  3. daily: those who said “once a day” or “several times a day”.

I initially ran cumulative logit models similar to those run for belief in god. However, the fitting procedure breaks in the VGLM funcion when trying to fit the model which allows all effects to be non-parallel, so I had to try some more constrained models.

Cumulative logit models predicting frequency of prayer
(1) (2) (3) (4) (5)
nonesNone -2.195*** -2.027*** -2.045***
(0.037) (0.071) (0.072)
year.centered 0.014*** 0.009*** 0.009***
(0.001) (0.002) (0.002)
year.spline 0.011* 0.011*
(0.005) (0.005)
nonesNone_year.centered -0.001 0.019* 0.020* 0.017*
(0.003) (0.008) (0.008) (0.008)
nonesNone_1 -2.312*** -2.162***
(0.038) (0.073)
nonesNone_2 -1.929*** -1.729***
(0.044) (0.074)
year.centered_1 0.013*** 0.008*
(0.001) (0.003)
year.centered_2 0.015*** 0.010***
(0.001) (0.003)
nonesNone_year.centered_1 -0.002
(0.004)
nonesNone_year.centered_2 0.005
(0.004)
year.spline_1 0.005
(0.006)
year.spline_2 0.012*
(0.005)
nonesNone_year.spline -0.036** -0.032* -0.035*
(0.014) (0.014) (0.014)
Observations 33056 33056 33056 33056 33056
BIC 60675.8 60518.9 60687.5 60681.8 60523.2
Note: p<0.05; p<0.01; p<0.001

This seems to show results consistent with those of the OLS regression models but it doesn’t allow for fully different effects at the weekly and daily cutpoints. This seems to be important as the fit of the models shown below indicates. For this figure I used model 5 for the spline model. The spline model can’t get the direction right for the weekly level. The fit is even worse in models 3 and 4.

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

## Warning in data.frame(..., check.names = FALSE): row names were found from
## a short variable and have been discarded

To remedy this I decided to estimate the cumulative logit models more primitively by just estimating two separate binary logit models at the two cutpoints.

Binary logit models predicting at least weekly prayer
(1) (2) (3) (4)
Calendar year -0.003* 0.013*** 0.013*** 0.011**
(0.001) (0.001) (0.001) (0.003)
No religious affiliation -2.321*** -2.312*** -2.187***
(0.036) (0.038) (0.077)
Year spline (>2000) 0.005
(0.006)
Year x No religious affiliation -0.002 0.012
(0.004) (0.009)
Year spline x No religious affiliation -0.027
(0.015)
BIC 37530.7 33038.2 33048.3 33066.4
Observations 33,056 33,056 33,056 33,056
Note: p<0.05; p<0.01; p<0.001
Binary logit models predicting at least daily prayer
(1) (2) (3) (4)
Calendar year 0.006*** 0.015*** 0.015*** 0.009***
(0.001) (0.001) (0.001) (0.003)
No religious affiliation -1.906*** -1.928*** -1.711***
(0.039) (0.044) (0.084)
Year spline (>2000) 0.012*
(0.005)
Year x No religious affiliation 0.005 0.032**
(0.004) (0.011)
Year spline x No religious affiliation -0.049**
(0.016)
BIC 47183.6 44204.3 44213.5 44225.8
Observations 33,056 33,056 33,056 33,056
Note: p<0.05; p<0.01; p<0.001

The results here are both consistent with the initial OLS regression estimates, but are considerably weaker for the weekly cutpoint. This suggests to me (along with the initial smoothed trend lines) that the important cutpoint is daily or less. Weekly is just a declining category for everybody. This should be fairly easy to capture in a multinomial model.

Multinomial logit models with non-believer as the reference category
weekly daily weekly daily
(1) (1) (2) (2)
year.centered 0.003 0.016*** 0.006 0.012***
(0.002) (0.001) (0.004) (0.003)
nonesNone -1.826*** -2.554*** -1.833*** -2.350***
(0.052) (0.046) (0.106) (0.089)
year.spline -0.007 0.009
(0.008) (0.007)
year.centered:nonesNone -0.005 0.003 -0.005 0.029**
(0.005) (0.004) (0.012) (0.011)
nonesNone:year.spline 0.001 -0.046**
(0.020) (0.017)
Constant 0.217*** 1.311*** 0.251*** 1.269***
(0.020) (0.016) (0.042) (0.036)
Note: p<0.05; p<0.01; p<0.001
Percent of respondents who prayed at a certain frequency, separated by those with a religious affilation and those without. LOWESS smoother shown for each trend based on weighted data. Fit of multinomial logit models with a linear trend (light grey) and a spline with a hinge at 2000 (dark grey) are also shown.

Percent of respondents who prayed at a certain frequency, separated by those with a religious affilation and those without. LOWESS smoother shown for each trend based on weighted data. Fit of multinomial logit models with a linear trend (light grey) and a spline with a hinge at 2000 (dark grey) are also shown.

Fits really nice now. Clear indication of non-linearity between less than once a week and daily. Polarization in two different ways. Polarization between the affiliated and unaffiliated since 2000. Polarization within each group by the decline in weekly prayers - Increasingly for both groups, you either pray daily of you don’t pray much at all (or at least thats what you say you do).

Birth Cohort Analysis

Lets take a look at where we get really small non-zero samples (n<20) by birth cohort and affiliation.

##     Year Affiliation Birthyear  n
## 11  1988   Religious 1970-1979  3
## 18  1993        None 1970-1979 16
## 47  1998        None 1980-1989  2
## 54  1998   Religious 1980-1989  4
## 90  2008        None 1990-1999  2
## 91  2008        None  pre-1940 16
## 97  2008   Religious 1990-1999  4
## 104 2010        None 1990-1999 10
## 105 2010        None  pre-1940 17
## 119 2012        None  pre-1940 13
## 133 2014        None  pre-1940 15

Most of these are cases where a young cohort has not fully aged into the sample. Lets just eliminate the cases of 10 or less for simplicity.

Now, I will look at the trend of each variable separately by cohort and affiliation. These plots may ba a little busy because I want to also include points in order to make sure one weird cohort is not skewing things.

## `geom_smooth()` using method = 'loess'
## Warning in sqrt(sum.squares/one.delta): NaNs produced
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : span too small. fewer data values than degrees of freedom.
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 2012
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 4.02
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : There are other near singularities as well. 16.16

## `geom_smooth()` using method = 'loess'
## Warning in sqrt(sum.squares/one.delta): NaNs produced
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : span too small. fewer data values than degrees of freedom.
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 2012
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 4.02
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : There are other near singularities as well. 16.16

## `geom_smooth()` using method = 'loess'
## Warning in sqrt(sum.squares/one.delta): NaNs produced
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : span too small. fewer data values than degrees of freedom.
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : pseudoinverse used at 2012
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : neighborhood radius 4.02
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : reciprocal condition number 0
## Warning in simpleLoess(y, x, w, span, degree = degree, parametric =
## parametric, : There are other near singularities as well. 16.16

There is some evidence of cohort trends for belief in god and prayer frequency in the manner that might be expected. The youngest cohorts have the lowest values and there hasn’t been nearly as much change across cohorts in the trends. This is not so for belief in the afterlife. There is also the interesting pattern tha the 1940-49 cohort tends to be one of the lowest consistently in all cases (The OG aethists). The baby boom cohorts and the 1970-79 seem to move similarly.

This all suggests to me that I might get more purchase on this if I group the birth cohorts as follows:

##            
##             before 1950 1950-1979 after 1979  <NA>
##   pre-1940        19446         0          0     0
##   1940-1949       10194         0          0     0
##   1950-1959           0     12712          0     0
##   1960-1969           0      9430          0     0
##   1970-1979           0      5819          0     0
##   1980-1989           0         0       3034     0
##   1990-1999           0         0        668     0
##   <NA>                0         0          0   192
## Warning: Removed 63 rows containing non-finite values (stat_smooth).
## Warning: Removed 63 rows containing missing values (geom_point).

Differences between the never affiliated and disaffiliated

Schwadel suggests that the percent of Americans who have grown up without a religious affiliation has grown considerably. We can therefore distinguish the never affiliated from the disaffiliated among our unaffiliated population. Its possible that the change in trend is driven by a changing composition within these groups and differences in belief. If the never affiliated are a larger proportion of the unaffiliated and they have lower levels of beliefs and practices then this would drive the overall effect down.

First lets look at the percentage of the never and disaffiliated over time.

## `geom_smooth()` using method = 'loess'

This is interesting, but also a bit puzzling. Why is the proportion never affiliated leveling off? If the proportion of the population raised without a religious preference is growing, we would expect the never affiliated to also grow absolutely, unless there is some weird religious revival going on among those raised with no religion in late 2000s. I don’t really have space to delve into this issue for this project, but should flag it for some future work.

One issue is that it appears the percent who report being raised without religion plateaued in the mid-2000s. This doesn’t seem to make a lot of sense given the rise in the nones but its a tricky thing to work out. It could reflect some complex birth cohort-fertility timing demographic trend or it might just reflect unreliable rememberances of what respondents experienced at age 16. I should do this by birth cohorts as well.

## `geom_smooth()` using method = 'loess'
## Warning: Removed 1 rows containing non-finite values (stat_smooth).
## Warning: Removed 1 rows containing missing values (geom_point).

So, the results by cohort make more sense.

Lets look at the share of never affiliated out of all unaffiliated as well.

## `geom_smooth()` using method = 'loess'

This proportion is rising thoughout the early period (pretty significantly) and then hits a ceiling in the mid-2000s before declining a bit. So, its unlikely that this can explain what is going on unless the never affiliated actually have stronger beliefs and practices.

Lets look at differences between the never affiliated and the disaffiliated

Trends in religious beliefs and practices among the religiously affiliated, the disaffiliated, and the never-affiliated. All ordinal questions are treated as a linear quantitative scale with a maximum of one and a minimum of zero. Smoothed (LOWESS) trend lines for each group are shown in light gray lines.

Trends in religious beliefs and practices among the religiously affiliated, the disaffiliated, and the never-affiliated. All ordinal questions are treated as a linear quantitative scale with a maximum of one and a minimum of zero. Smoothed (LOWESS) trend lines for each group are shown in light gray lines.

Linear regression models predicting strength of belief in god
Strength of belief in god
(1) (2) (3)
Year -0.0002 -0.0001 0.0011
(0.0002) (0.0002) (0.0006)
Year spline (>2000) -0.0019*
(0.0009)
Never affiliated -0.3767*** -0.3555*** -0.3343***
(0.0085) (0.0120) (0.0214)
Disaffiliated -0.3842*** -0.3785*** -0.3626***
(0.0052) (0.0070) (0.0134)
Year x Never -0.0028* 0.0019
(0.0011) (0.0037)
Year x Disaffiliated -0.0008 0.0025
(0.0006) (0.0022)
Year spline x Never -0.0065
(0.0051)
Year spline x Disaffiliated -0.0046
(0.0031)
Constant 0.8800*** 0.8793*** 0.8872***
(0.0019) (0.0020) (0.0043)
Observations 22,228 22,228 22,228
R2 0.2414 0.2416 0.2420
Note: p<0.05; p<0.01; p<0.001
Linear regression models predicting strength of belief in afterlife
Strength of belief in afterlife
(1) (2) (3)
Year 0.0017*** 0.0018*** 0.0021***
(0.0001) (0.0001) (0.0003)
Year spline (>2000) -0.0011
(0.0006)
Never affiliated -0.2758*** -0.2747*** -0.2525***
(0.0104) (0.0106) (0.0195)
Disaffiliated -0.2556*** -0.2556*** -0.2119***
(0.0063) (0.0063) (0.0125)
Year x Never -0.0006 0.0016
(0.0009) (0.0018)
Year x Disaffiliated -0.0003 0.0031***
(0.0005) (0.0010)
Year spline x Never -0.0046
(0.0034)
Year spline x Disaffiliated -0.0079***
(0.0020)
Constant 0.8117*** 0.8119*** 0.8173***
(0.0020) (0.0021) (0.0038)
Observations 44,354 44,354 44,354
R2 0.0483 0.0483 0.0489
Note: p<0.05; p<0.01; p<0.001
Linear regression models predicting frequency of prayer
Frequency of prayer
(1) (2) (3)
Year 0.0027*** 0.0027*** 0.0019***
(0.0002) (0.0002) (0.0004)
Year spline (>2000) 0.0016
(0.0008)
Never affiliated -0.4434*** -0.4408*** -0.4137***
(0.0105) (0.0116) (0.0218)
Disaffiliated -0.3948*** -0.3944*** -0.3651***
(0.0065) (0.0070) (0.0143)
Year x Never -0.0006 0.0027
(0.0011) (0.0027)
Year x Disaffiliated -0.0001 0.0032*
(0.0006) (0.0016)
Year spline x Never -0.0061
(0.0043)
Year spline x Disaffiliated -0.0062*
(0.0027)
Constant 0.6264*** 0.6264*** 0.6185***
(0.0021) (0.0021) (0.0046)
Observations 32,967 32,967 32,967
R2 0.1341 0.1341 0.1344
Note: p<0.05; p<0.01; p<0.001
Linear regression models predicting frequency of attendance
Frequency of attendance
(1) (2) (3)
Year -0.0004*** -0.0006*** -0.0007***
(0.0001) (0.0001) (0.0002)
Year spline (>2000) 0.0003
(0.0005)
Never affiliated -0.4348*** -0.4355*** -0.4272***
(0.0078) (0.0078) (0.0139)
Disaffiliated -0.4038*** -0.4022*** -0.4017***
(0.0047) (0.0047) (0.0089)
Year x Never 0.0013 0.0021
(0.0007) (0.0013)
Year x Disaffiliated 0.0010** 0.0010
(0.0004) (0.0007)
Year spline x Never -0.0018
(0.0025)
Year spline x Disaffiliated -0.0001
(0.0014)
Constant 0.5198*** 0.5190*** 0.5176***
(0.0015) (0.0015) (0.0027)
Observations 57,835 57,835 57,835
R2 0.1528 0.1529 0.1529
Note: p<0.05; p<0.01; p<0.001